A few tidbits on the 15
The class 15 was made 1890-1957 "K" simply designates Kilibowe - where it was made. When Singer moved to the Anderson plant, they started putting A after machines, most with no letter were made at Elisabethport. J is Canada, G is Germany - and I think there are more. Early on it was mostly "nothing" for US and K for UK. However this was not always put on the machine . . .
The early 15 type was made 1895 to 1933, The most notable feature is the LACK of reverse, instead there is a small knob for the stitch width. Came in assorted decal patterns. There were variations, and Singer also used the -XX to designate options, sometimes they weren't much of a difference. A lot of 15-xx machines are industrial - part of what leads to confusion on sellers claiming Singer 15's are industrial - because many are. And some look the same except they used heavier components underneath.
Notice the knob on the pillar - this is a 1935 model (K made) BTW - this one has a 1 o'clock bobbin case finger
ISMACS site has a good list of all the models and variations - some I have no idea, one has "Long beak shuttle, some don't have drop feed.
This is another 15 of that type, but much older (the one on the right). The one on the left is a 115 - they are the same on the top side.
Though this isn't the best picture to show it, this one also has the 1 o'clock case finger.
It also shows the significant difference between a 115 and 15
The other group is the 15-88, 89, 90, 91 group - and it has the reverse and stitch length lever. The -XX denotes the power source. The first three are the same machine, the last has the potted motor so the frame is a bit different. The Treadle/hand crank versions have a spoked handwheel while the 90 has a solid wheel as the spokes are not needed. However you can easily put a motor on an 88/89 with no problems. This model has an 11 o'clock bobbin case finger.
the left is a 15-90 and the right is an early 15-91 with the silver plate. That was only used for a limited time at the start of production of this type machine, then they all switched to the black plate.
This is a 15-75, updated frame but basically the same machine as the 15-90